Load Data

# Load Data
source(here('scripts', 'Other_Functions.R'))
data <- load_processed_data_all_conditions()
data_long <- load_processed_data_all_conditions_long()
data_long$Condition_num <- as.numeric(data_long$Condition)

# Figure Parameters
source(here('scripts', 'Figure_Parameters.R'))

# Data manipulation
data_long$Reliability_factor <- as.factor(data_long$Reliability)
data_long$Block_factor <- as.factor(data_long$Block)

# Subsets
data_long_50 <-  data_long %>% 
  filter(Condition == '50% Decreasing' | Condition == '50% Increasing')
# remove the other possible factors
data_long_50$Condition <- factor(data_long_50$Condition, levels = c('50% Decreasing', '50% Increasing'))
# repalce with 1 or 2
data_long_50$Condition_num <- as.numeric(data_long_50$Condition)

data_long_70 <-  data_long %>%
  filter(Condition == '70% Decreasing' | Condition == '70% Increasing')
# remove the other possible factors
data_long_70$Condition <- factor(data_long_70$Condition, levels = c('70% Decreasing', '70% Increasing'))
# repalce with 1 or 2
data_long_70$Condition_num <- as.numeric(data_long_70$Condition)

Basic Visuals

Histograms

# ggplot histogram of trust
g1 <- ggplot(data_long, aes(x=Trust)) + 
  geom_histogram(position = "dodge", bins = 100) +
  theme_classic() +
  labs(title = "Trust", x = "Trust", y = "Frequency") 
print(g1)

# ggplot histogram of confidence
g2 <- ggplot(data_long, aes(x=Confidence)) + 
  geom_histogram(position = "dodge", bins = 100) +
  theme_classic() +
  labs(title = "Confidence", x = "Confidence", y = "Frequency")
print(g2)

# ggplot histogram of reliance
g3 <- ggplot(data_long, aes(x=Reliance)) + 
  geom_histogram(position = "dodge", bins = 100) +
  theme_classic() +
  labs(title = "Reliance", x = "Reliance", y = "Frequency")
print(g3)

Correlations

# Show Correlations
cor <- cor(data_long[,c("Trust", "Reliability", "Confidence", "Reliance", "Condition_num", "Performance_Before", "Performance_After")])
corrplot(cor, method = "circle")

Data Checks

# Assumptions
# Normality
qqnorm(data_long$Trust)
qqline(data_long$Trust)

qqnorm(data_long$Confidence)
qqline(data_long$Confidence)

qqnorm(data_long$Reliance)
qqline(data_long$Reliance)

# Homoscedasticity
plot(data_long$Trust ~ data_long$Reliability)

plot(data_long$Trust ~ data_long$Confidence)

plot(data_long$Trust ~ data_long$Reliance)

plot(data_long$Trust ~ data_long$Performance_After)

plot(data_long$Reliance ~ data_long$Reliability)

plot(data_long$Reliance ~ data_long$Confidence)

plot(data_long$Reliance ~ data_long$Performance_After)

plot(data_long$Confidence ~ data_long$Reliability)

plot(data_long$Confidence ~ data_long$Performance_After)

plot(data_long$Performance_After ~ data_long$Reliability)

# Sphericity
shapiro.test(data_long$Trust)

## 
##  Shapiro-Wilk normality test
## 
## data:  data_long$Trust
## W = 0.96534, p-value = 2.168e-14

shapiro.test(data_long$Confidence)

## 
##  Shapiro-Wilk normality test
## 
## data:  data_long$Confidence
## W = 0.93476, p-value < 2.2e-16

shapiro.test(data_long$Reliance)

## 
##  Shapiro-Wilk normality test
## 
## data:  data_long$Reliance
## W = 0.87745, p-value < 2.2e-16

shapiro.test(data_long$Performance_Before)

## 
##  Shapiro-Wilk normality test
## 
## data:  data_long$Performance_Before
## W = 0.98875, p-value = 9.285e-07

shapiro.test(data_long$Performance_After)

## 
##  Shapiro-Wilk normality test
## 
## data:  data_long$Performance_After
## W = 0.96795, p-value = 9.419e-14

50% Models

Trust

Model

# Everything Model
m50_1 <- lmer(data = data_long_50, Trust ~ Condition * Reliability * Confidence * Reliance * (1 | Participant))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(m50_1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Trust ~ Condition * Reliability * Confidence * Reliance * (1 |  
##     Participant)
##    Data: data_long_50
## 
## REML criterion at convergence: 3036.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.8792 -0.4320 -0.0012  0.4522  3.0305 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Participant (Intercept) 74.17    8.612   
##  Residual                17.11    4.136   
## Number of obs: 480, groups:  Participant, 80
## 
## Fixed effects:
##                                                           Estimate Std. Error
## (Intercept)                                              46.276500  13.572137
## Condition50% Increasing                                 -16.186487  19.277093
## Reliability                                              -0.064241   0.183336
## Confidence                                                0.356908   0.153062
## Reliance                                                -52.982108  35.367254
## Condition50% Increasing:Reliability                       0.140755   0.235453
## Condition50% Increasing:Confidence                        0.206110   0.220458
## Reliability:Confidence                                    0.001160   0.002079
## Condition50% Increasing:Reliance                         92.633649  45.660402
## Reliability:Reliance                                      0.649169   0.437598
## Confidence:Reliance                                       0.635282   0.404977
## Condition50% Increasing:Reliability:Confidence           -0.001624   0.002706
## Condition50% Increasing:Reliability:Reliance             -1.095827   0.552562
## Condition50% Increasing:Confidence:Reliance              -0.995395   0.523430
## Reliability:Confidence:Reliance                          -0.007611   0.005002
## Condition50% Increasing:Reliability:Confidence:Reliance   0.011775   0.006329
##                                                         t value
## (Intercept)                                               3.410
## Condition50% Increasing                                  -0.840
## Reliability                                              -0.350
## Confidence                                                2.332
## Reliance                                                 -1.498
## Condition50% Increasing:Reliability                       0.598
## Condition50% Increasing:Confidence                        0.935
## Reliability:Confidence                                    0.558
## Condition50% Increasing:Reliance                          2.029
## Reliability:Reliance                                      1.483
## Confidence:Reliance                                       1.569
## Condition50% Increasing:Reliability:Confidence           -0.600
## Condition50% Increasing:Reliability:Reliance             -1.983
## Condition50% Increasing:Confidence:Reliance              -1.902
## Reliability:Confidence:Reliance                          -1.522
## Condition50% Increasing:Reliability:Confidence:Reliance   1.861

## 
## Correlation matrix not shown by default, as p = 16 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

tab_model(m50_1)

	Trust
Predictors	Estimates	CI	p
(Intercept)	46.28	19.61 – 72.95	0.001
Condition [50% Increasing]	-16.19	-54.07 – 21.70	0.402
Reliability	-0.06	-0.42 – 0.30	0.726
Confidence	0.36	0.06 – 0.66	0.020
Reliance	-52.98	-122.48 – 16.52	0.135
Condition [50% Increasing] × Reliability	0.14	-0.32 – 0.60	0.550
Condition [50% Increasing] × Confidence	0.21	-0.23 – 0.64	0.350
Reliability × Confidence	0.00	-0.00 – 0.01	0.577
Condition [50% Increasing] × Reliance	92.63	2.91 – 182.36	0.043
Reliability × Reliance	0.65	-0.21 – 1.51	0.139
Confidence × Reliance	0.64	-0.16 – 1.43	0.117
(Condition [50% Increasing] × Reliability) × Confidence	-0.00	-0.01 – 0.00	0.549
(Condition [50% Increasing] × Reliability) × Reliance	-1.10	-2.18 – -0.01	0.048
(Condition [50% Increasing] × Confidence) × Reliance	-1.00	-2.02 – 0.03	0.058
(Reliability × Confidence) × Reliance	-0.01	-0.02 – 0.00	0.129
(Condition [50% Increasing] × Reliability × Confidence) × Reliance	0.01	-0.00 – 0.02	0.063
Random Effects
σ²	17.11
τ₀₀ _Participant	74.17
ICC	0.81
N _Participant	80
Observations	480
Marginal R² / Conditional R²	0.301 / 0.869

Visualizations

# Visualize Trust by Confidence
g1 <- ggplot(data_long_50, aes(x=Confidence, y=Trust)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Trust by Confidence", x = "Confidence", y = "Trust") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 100) + 
  ylim(0, 100)
print(g1)

## `geom_smooth()` using formula = 'y ~ x'

# Visualize Interactions (Condition, Reliance)
g2 <- ggplot(data_long_50, aes(x=Reliance, y=Trust, color=Condition)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Trust by Reliance by Condition", x = "Reliance", y = "Trust") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 1) + 
  ylim(0, 100)
print(g2)

## `geom_smooth()` using formula = 'y ~ x'

# Visualize Interactions (Condition, Reliability, Reliance)
g3 <- ggplot(data_long_50, aes(x=Reliance, y=Trust, color=Reliability_factor, group=Reliability_factor)) + 
  geom_smooth(alpha = 0.1, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Trust by Reliance by Reliability", x = "Reliance", y = "Trust") +
  theme(plot.title = element_text(size=title_size)) +
  facet_wrap(~Condition) +
  xlim(0, 1) + 
  ylim(0, 100)
print(g3)

## `geom_smooth()` using formula = 'y ~ x'

# Visualize most complex interaction (just for fun)
# g4 <- ggplot(data_long_50, aes(x=Reliance, y=Trust, color=Reliability_factor, group=Reliability_factor)) + 
#   geom_smooth(alpha = 0.1, method = 'lm') + 
#   geom_point() +
#   theme_classic() +
#   labs(title = "Trust by Reliance by Reliability", x = "Reliance", y = "Trust") +
#   theme(plot.title = element_text(size=title_size)) +
#   facet_wrap(~Condition * Reliability_factor) +
#   xlim(0, 1) + 
#   ylim(0, 100)
# print(g4)

flexplot(data = data_long_50, Trust ~ Reliance + Reliability_factor | Condition + Confidence, method = 'lm')

Dependence (Reliance)

Model

# Everything Model
m50_2 <- lmer(data = data_long_50, Reliance ~ Condition * Reliability * Confidence * Trust * (1 | Participant))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(m50_2)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Reliance ~ Condition * Reliability * Confidence * Trust * (1 |  
##     Participant)
##    Data: data_long_50
## 
## REML criterion at convergence: -16.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9338 -0.4904 -0.0450  0.4329  4.1183 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Participant (Intercept) 0.10096  0.3177  
##  Residual                0.02064  0.1437  
## Number of obs: 480, groups:  Participant, 80
## 
## Fixed effects:
##                                                        Estimate Std. Error
## (Intercept)                                          -3.904e+00  1.644e+00
## Condition50% Increasing                               5.890e+00  2.237e+00
## Reliability                                           6.131e-02  2.057e-02
## Confidence                                            4.138e-02  1.842e-02
## Trust                                                 5.605e-02  2.440e-02
## Condition50% Increasing:Reliability                  -7.959e-02  2.697e-02
## Condition50% Increasing:Confidence                   -5.273e-02  2.646e-02
## Reliability:Confidence                               -6.265e-04  2.330e-04
## Condition50% Increasing:Trust                        -8.274e-02  3.218e-02
## Reliability:Trust                                    -7.470e-04  2.976e-04
## Confidence:Trust                                     -5.697e-04  2.598e-04
## Condition50% Increasing:Reliability:Confidence        7.024e-04  3.198e-04
## Condition50% Increasing:Reliability:Trust             1.016e-03  3.868e-04
## Condition50% Increasing:Confidence:Trust              7.625e-04  3.544e-04
## Reliability:Confidence:Trust                          7.822e-06  3.200e-06
## Condition50% Increasing:Reliability:Confidence:Trust -8.944e-06  4.255e-06
##                                                      t value
## (Intercept)                                           -2.374
## Condition50% Increasing                                2.632
## Reliability                                            2.980
## Confidence                                             2.247
## Trust                                                  2.298
## Condition50% Increasing:Reliability                   -2.951
## Condition50% Increasing:Confidence                    -1.993
## Reliability:Confidence                                -2.688
## Condition50% Increasing:Trust                         -2.571
## Reliability:Trust                                     -2.510
## Confidence:Trust                                      -2.192
## Condition50% Increasing:Reliability:Confidence         2.196
## Condition50% Increasing:Reliability:Trust              2.626
## Condition50% Increasing:Confidence:Trust               2.151
## Reliability:Confidence:Trust                           2.445
## Condition50% Increasing:Reliability:Confidence:Trust  -2.102

## 
## Correlation matrix not shown by default, as p = 16 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

tab_model(m50_2)

	Reliance
Predictors	Estimates	CI	p
(Intercept)	-3.90	-7.14 – -0.67	0.018
Condition [50% Increasing]	5.89	1.49 – 10.29	0.009
Reliability	0.06	0.02 – 0.10	0.003
Confidence	0.04	0.01 – 0.08	0.025
Trust	0.06	0.01 – 0.10	0.022
Condition [50% Increasing] × Reliability	-0.08	-0.13 – -0.03	0.003
Condition [50% Increasing] × Confidence	-0.05	-0.10 – -0.00	0.047
Reliability × Confidence	-0.00	-0.00 – -0.00	0.007
Condition [50% Increasing] × Trust	-0.08	-0.15 – -0.02	0.010
Reliability × Trust	-0.00	-0.00 – -0.00	0.012
Confidence × Trust	-0.00	-0.00 – -0.00	0.029
(Condition [50% Increasing] × Reliability) × Confidence	0.00	0.00 – 0.00	0.029
(Condition [50% Increasing] × Reliability) × Trust	0.00	0.00 – 0.00	0.009
(Condition [50% Increasing] × Confidence) × Trust	0.00	0.00 – 0.00	0.032
(Reliability × Confidence) × Trust	0.00	0.00 – 0.00	0.015
(Condition [50% Increasing] × Reliability × Confidence) × Trust	-0.00	-0.00 – -0.00	0.036
Random Effects
σ²	0.02
τ₀₀ _Participant	0.10
ICC	0.83
N _Participant	80
Observations	480
Marginal R² / Conditional R²	0.046 / 0.838

Visualizations

# Visualize Dependence by Trust
g1 <- ggplot(data_long_50, aes(x=Trust, y=Reliance)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Dependence by Trust", x = "Trust", y = "Dependence") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 100) + 
  ylim(0, 1)
print(g1)

## `geom_smooth()` using formula = 'y ~ x'

# Visualize Dependence by Trust and Condition
g2 <- ggplot(data_long_50, aes(x=Trust, y=Reliance, color=Condition)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Dependence by Trust by Condition", x = "Trust", y = "Dependence") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 100) + 
  ylim(0, 1)
print(g2)

## `geom_smooth()` using formula = 'y ~ x'

# Visualize Dependence by Trust and Reliability
g3 <- ggplot(data_long_50, aes(x=Trust, y=Reliance, color=Reliability_factor, group=Reliability_factor)) + 
  geom_smooth(alpha = 0.1, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Dependence by Trust by Reliability", x = "Trust", y = "Dependence") +
  theme(plot.title = element_text(size=title_size)) +
  facet_wrap(~Condition) +
  xlim(0, 100) + 
  ylim(0, 1)
print(g3)

## `geom_smooth()` using formula = 'y ~ x'

# Remove Reliability and add Confidence
flexplot(data = data_long_50, Reliance ~ Trust + Confidence | Condition, method = 'lm', se = TRUE)

# Visualize most complex interaction 
flexplot(data = data_long_50, Reliance ~ Trust + Reliability_factor | Condition + Confidence, method = 'lm')

Performance

Model

# Everything Model
m50_3 <- lmer(data = data_long_50, Performance_After ~ Condition * Reliability * Confidence * Trust * Reliance * (1 | Participant))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(m50_3)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Performance_After ~ Condition * Reliability * Confidence * Trust *  
##     Reliance * (1 | Participant)
##    Data: data_long_50
## 
## REML criterion at convergence: -584.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4197 -0.5144 -0.0200  0.5663  2.6916 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Participant (Intercept) 0.011427 0.10690 
##  Residual                0.004294 0.06553 
## Number of obs: 480, groups:  Participant, 80
## 
## Fixed effects:
##                                                                 Estimate
## (Intercept)                                                    2.391e+00
## Condition50% Increasing                                       -9.952e-01
## Reliability                                                   -1.678e-02
## Confidence                                                    -1.368e-02
## Trust                                                         -2.810e-02
## Reliance                                                      -2.773e-01
## Condition50% Increasing:Reliability                            1.135e-02
## Condition50% Increasing:Confidence                            -1.461e-03
## Reliability:Confidence                                         1.151e-04
## Condition50% Increasing:Trust                                  1.186e-02
## Reliability:Trust                                              2.852e-04
## Confidence:Trust                                               2.638e-04
## Condition50% Increasing:Reliance                              -1.122e+00
## Reliability:Reliance                                           1.570e-02
## Confidence:Reliance                                           -1.742e-02
## Trust:Reliance                                                 2.089e-02
## Condition50% Increasing:Reliability:Confidence                 3.644e-05
## Condition50% Increasing:Reliability:Trust                     -2.043e-04
## Condition50% Increasing:Confidence:Trust                       8.118e-06
## Reliability:Confidence:Trust                                  -2.370e-06
## Condition50% Increasing:Reliability:Reliance                  -1.965e-03
## Condition50% Increasing:Confidence:Reliance                    4.439e-02
## Reliability:Confidence:Reliance                                6.345e-05
## Condition50% Increasing:Trust:Reliance                         6.590e-03
## Reliability:Trust:Reliance                                    -3.542e-04
## Confidence:Trust:Reliance                                     -9.137e-05
## Condition50% Increasing:Reliability:Confidence:Trust           4.747e-07
## Condition50% Increasing:Reliability:Confidence:Reliance       -3.679e-04
## Condition50% Increasing:Reliability:Trust:Reliance             1.540e-04
## Condition50% Increasing:Confidence:Trust:Reliance             -4.235e-04
## Reliability:Confidence:Trust:Reliance                          2.351e-06
## Condition50% Increasing:Reliability:Confidence:Trust:Reliance  2.524e-06
##                                                               Std. Error
## (Intercept)                                                    1.190e+00
## Condition50% Increasing                                        1.608e+00
## Reliability                                                    1.673e-02
## Confidence                                                     1.300e-02
## Trust                                                          1.680e-02
## Reliance                                                       3.558e+00
## Condition50% Increasing:Reliability                            2.070e-02
## Condition50% Increasing:Confidence                             1.835e-02
## Reliability:Confidence                                         1.848e-04
## Condition50% Increasing:Trust                                  2.284e-02
## Reliability:Trust                                              2.285e-04
## Confidence:Trust                                               1.775e-04
## Condition50% Increasing:Reliance                               4.542e+00
## Reliability:Reliance                                           4.478e-02
## Confidence:Reliance                                            3.996e-02
## Trust:Reliance                                                 4.760e-02
## Condition50% Increasing:Reliability:Confidence                 2.332e-04
## Condition50% Increasing:Reliability:Trust                      2.928e-04
## Condition50% Increasing:Confidence:Trust                       2.463e-04
## Reliability:Confidence:Trust                                   2.446e-06
## Condition50% Increasing:Reliability:Reliance                   5.632e-02
## Condition50% Increasing:Confidence:Reliance                    5.386e-02
## Reliability:Confidence:Reliance                                5.041e-04
## Condition50% Increasing:Trust:Reliance                         5.918e-02
## Reliability:Trust:Reliance                                     5.978e-04
## Confidence:Trust:Reliance                                      5.106e-04
## Condition50% Increasing:Reliability:Confidence:Trust           3.127e-06
## Condition50% Increasing:Reliability:Confidence:Reliance        6.695e-04
## Condition50% Increasing:Reliability:Trust:Reliance             7.323e-04
## Condition50% Increasing:Confidence:Trust:Reliance              6.571e-04
## Reliability:Confidence:Trust:Reliance                          6.457e-06
## Condition50% Increasing:Reliability:Confidence:Trust:Reliance  8.173e-06
##                                                               t value
## (Intercept)                                                     2.009
## Condition50% Increasing                                        -0.619
## Reliability                                                    -1.003
## Confidence                                                     -1.052
## Trust                                                          -1.672
## Reliance                                                       -0.078
## Condition50% Increasing:Reliability                             0.548
## Condition50% Increasing:Confidence                             -0.080
## Reliability:Confidence                                          0.623
## Condition50% Increasing:Trust                                   0.519
## Reliability:Trust                                               1.248
## Confidence:Trust                                                1.486
## Condition50% Increasing:Reliance                               -0.247
## Reliability:Reliance                                            0.351
## Confidence:Reliance                                            -0.436
## Trust:Reliance                                                  0.439
## Condition50% Increasing:Reliability:Confidence                  0.156
## Condition50% Increasing:Reliability:Trust                      -0.698
## Condition50% Increasing:Confidence:Trust                        0.033
## Reliability:Confidence:Trust                                   -0.969
## Condition50% Increasing:Reliability:Reliance                   -0.035
## Condition50% Increasing:Confidence:Reliance                     0.824
## Reliability:Confidence:Reliance                                 0.126
## Condition50% Increasing:Trust:Reliance                          0.111
## Reliability:Trust:Reliance                                     -0.593
## Confidence:Trust:Reliance                                      -0.179
## Condition50% Increasing:Reliability:Confidence:Trust            0.152
## Condition50% Increasing:Reliability:Confidence:Reliance        -0.550
## Condition50% Increasing:Reliability:Trust:Reliance              0.210
## Condition50% Increasing:Confidence:Trust:Reliance              -0.644
## Reliability:Confidence:Trust:Reliance                           0.364
## Condition50% Increasing:Reliability:Confidence:Trust:Reliance   0.309

## 
## Correlation matrix not shown by default, as p = 32 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

tab_model(m50_3)

	Performance After
Predictors	Estimates	CI	p
(Intercept)	2.39	0.05 – 4.73	0.045
Condition [50% Increasing]	-1.00	-4.16 – 2.16	0.536
Reliability	-0.02	-0.05 – 0.02	0.317
Confidence	-0.01	-0.04 – 0.01	0.293
Trust	-0.03	-0.06 – 0.00	0.095
Reliance	-0.28	-7.27 – 6.72	0.938
Condition [50% Increasing] × Reliability	0.01	-0.03 – 0.05	0.584
Condition [50% Increasing] × Confidence	-0.00	-0.04 – 0.03	0.937
Reliability × Confidence	0.00	-0.00 – 0.00	0.534
Condition [50% Increasing] × Trust	0.01	-0.03 – 0.06	0.604
Reliability × Trust	0.00	-0.00 – 0.00	0.213
Confidence × Trust	0.00	-0.00 – 0.00	0.138
Condition [50% Increasing] × Reliance	-1.12	-10.05 – 7.80	0.805
Reliability × Reliance	0.02	-0.07 – 0.10	0.726
Confidence × Reliance	-0.02	-0.10 – 0.06	0.663
Trust × Reliance	0.02	-0.07 – 0.11	0.661
(Condition [50% Increasing] × Reliability) × Confidence	0.00	-0.00 – 0.00	0.876
(Condition [50% Increasing] × Reliability) × Trust	-0.00	-0.00 – 0.00	0.486
(Condition [50% Increasing] × Confidence) × Trust	0.00	-0.00 – 0.00	0.974
(Reliability × Confidence) × Trust	-0.00	-0.00 – 0.00	0.333
(Condition [50% Increasing] × Reliability) × Reliance	-0.00	-0.11 – 0.11	0.972
(Condition [50% Increasing] × Confidence) × Reliance	0.04	-0.06 – 0.15	0.410
(Reliability × Confidence) × Reliance	0.00	-0.00 – 0.00	0.900
(Condition [50% Increasing] × Trust) × Reliance	0.01	-0.11 – 0.12	0.911
(Reliability × Trust) × Reliance	-0.00	-0.00 – 0.00	0.554
(Confidence × Trust) × Reliance	-0.00	-0.00 – 0.00	0.858
(Condition [50% Increasing] × Reliability × Confidence) × Trust	0.00	-0.00 – 0.00	0.879
(Condition [50% Increasing] × Reliability × Confidence) × Reliance	-0.00	-0.00 – 0.00	0.583
(Condition [50% Increasing] × Reliability × Trust) × Reliance	0.00	-0.00 – 0.00	0.833
(Condition [50% Increasing] × Confidence × Trust) × Reliance	-0.00	-0.00 – 0.00	0.520
(Reliability × Confidence × Trust) × Reliance	0.00	-0.00 – 0.00	0.716
(Condition [50% Increasing] × Reliability × Confidence × Trust) × Reliance	0.00	-0.00 – 0.00	0.758
Random Effects
σ²	0.00
τ₀₀ _Participant	0.01
ICC	0.73
N _Participant	80
Observations	480
Marginal R² / Conditional R²	0.334 / 0.818

Visualizations

# trust by performance
g1 <- ggplot(data_long_50, aes(x=Trust, y=Performance_After)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Performance After by Trust by Condition", x = "Trust", y = "Performance After") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 100) + 
  ylim(0, 1)
print(g1)

## `geom_smooth()` using formula = 'y ~ x'

70% Models

Trust

Model

# Everything Model
m70_1 <- lmer(data = data_long_70, Trust ~ Condition * Reliability * Confidence * Reliance * (1 | Participant))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(m70_1)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Trust ~ Condition * Reliability * Confidence * Reliance * (1 |  
##     Participant)
##    Data: data_long_70
## 
## REML criterion at convergence: 3147.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.1663 -0.4908  0.0266  0.5266  4.5948 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Participant (Intercept) 78.09    8.837   
##  Residual                20.66    4.546   
## Number of obs: 486, groups:  Participant, 81
## 
## Fixed effects:
##                                                           Estimate Std. Error
## (Intercept)                                              50.543933  27.169845
## Condition70% Increasing                                 -21.852125  34.026793
## Reliability                                              -0.348433   0.324246
## Confidence                                                0.222184   0.312859
## Reliance                                                -94.298837  59.674490
## Condition70% Increasing:Reliability                       0.349005   0.393641
## Condition70% Increasing:Confidence                        0.334764   0.395000
## Reliability:Confidence                                    0.005676   0.003745
## Condition70% Increasing:Reliance                        155.216558  72.193542
## Reliability:Reliance                                      1.223567   0.698786
## Confidence:Reliance                                       1.331890   0.679141
## Condition70% Increasing:Reliability:Confidence           -0.005288   0.004567
## Condition70% Increasing:Reliability:Reliance             -1.708054   0.826693
## Condition70% Increasing:Confidence:Reliance              -1.981159   0.833851
## Reliability:Confidence:Reliance                          -0.016796   0.007905
## Condition70% Increasing:Reliability:Confidence:Reliance   0.022030   0.009494
##                                                         t value
## (Intercept)                                               1.860
## Condition70% Increasing                                  -0.642
## Reliability                                              -1.075
## Confidence                                                0.710
## Reliance                                                 -1.580
## Condition70% Increasing:Reliability                       0.887
## Condition70% Increasing:Confidence                        0.848
## Reliability:Confidence                                    1.516
## Condition70% Increasing:Reliance                          2.150
## Reliability:Reliance                                      1.751
## Confidence:Reliance                                       1.961
## Condition70% Increasing:Reliability:Confidence           -1.158
## Condition70% Increasing:Reliability:Reliance             -2.066
## Condition70% Increasing:Confidence:Reliance              -2.376
## Reliability:Confidence:Reliance                          -2.125
## Condition70% Increasing:Reliability:Confidence:Reliance   2.320

## 
## Correlation matrix not shown by default, as p = 16 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

tab_model(m70_1)

	Trust
Predictors	Estimates	CI	p
(Intercept)	50.54	-2.85 – 103.93	0.063
Condition [70% Increasing]	-21.85	-88.72 – 45.01	0.521
Reliability	-0.35	-0.99 – 0.29	0.283
Confidence	0.22	-0.39 – 0.84	0.478
Reliance	-94.30	-211.56 – 22.96	0.115
Condition [70% Increasing] × Reliability	0.35	-0.42 – 1.12	0.376
Condition [70% Increasing] × Confidence	0.33	-0.44 – 1.11	0.397
Reliability × Confidence	0.01	-0.00 – 0.01	0.130
Condition [70% Increasing] × Reliance	155.22	13.35 – 297.08	0.032
Reliability × Reliance	1.22	-0.15 – 2.60	0.081
Confidence × Reliance	1.33	-0.00 – 2.67	0.050
(Condition [70% Increasing] × Reliability) × Confidence	-0.01	-0.01 – 0.00	0.247
(Condition [70% Increasing] × Reliability) × Reliance	-1.71	-3.33 – -0.08	0.039
(Condition [70% Increasing] × Confidence) × Reliance	-1.98	-3.62 – -0.34	0.018
(Reliability × Confidence) × Reliance	-0.02	-0.03 – -0.00	0.034
(Condition [70% Increasing] × Reliability × Confidence) × Reliance	0.02	0.00 – 0.04	0.021
Random Effects
σ²	20.66
τ₀₀ _Participant	78.09
ICC	0.79
N _Participant	81
Observations	486
Marginal R² / Conditional R²	0.400 / 0.874

Visualizations

# Visualize Condition by reliance
g1 <- ggplot(data_long_70, aes(x=Reliance, y=Trust, color=Condition)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Trust by Reliance by Condition", x = "Reliance", y = "Trust") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 1) + 
  ylim(0, 100)
print(g1)

## `geom_smooth()` using formula = 'y ~ x'

# Condition bu Reliability by Reliance
g2 <- ggplot(data_long_70, aes(x=Reliance, y=Trust, color=Reliability_factor, group=Reliability_factor)) + 
  geom_smooth(alpha = 0.1, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Trust by Reliance by Reliability", x = "Reliance", y = "Trust") +
  theme(plot.title = element_text(size=title_size)) +
  facet_wrap(~Condition) +
  xlim(0, 1) + 
  ylim(0, 100)
print(g2)

## `geom_smooth()` using formula = 'y ~ x'

# Condition by Reliability by Reliance by Confidence
flexplot(data = data_long_70, Trust ~ Reliance + Reliability_factor | Condition + Confidence, method = 'lm')

Dependence (Reliance)

Model

# Everything Model
m70_2 <- lmer(data = data_long_70, Reliance ~ Condition * Reliability * Confidence * Trust * (1 | Participant))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(m70_2)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Reliance ~ Condition * Reliability * Confidence * Trust * (1 |  
##     Participant)
##    Data: data_long_70
## 
## REML criterion at convergence: 52
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0740 -0.4960 -0.0191  0.5240  3.3555 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Participant (Intercept) 0.09502  0.3082  
##  Residual                0.02520  0.1587  
## Number of obs: 486, groups:  Participant, 81
## 
## Fixed effects:
##                                                        Estimate Std. Error
## (Intercept)                                          -6.846e-01  2.560e+00
## Condition70% Increasing                              -1.410e+00  3.418e+00
## Reliability                                           7.159e-03  3.085e-02
## Confidence                                            1.333e-02  3.395e-02
## Trust                                                 3.118e-02  3.409e-02
## Condition70% Increasing:Reliability                   1.396e-02  4.024e-02
## Condition70% Increasing:Confidence                    2.361e-02  4.460e-02
## Reliability:Confidence                               -1.030e-04  4.116e-04
## Condition70% Increasing:Trust                        -2.484e-03  4.640e-02
## Reliability:Trust                                    -3.072e-04  4.036e-04
## Confidence:Trust                                     -3.859e-04  4.168e-04
## Condition70% Increasing:Reliability:Confidence       -2.650e-04  5.250e-04
## Condition70% Increasing:Reliability:Trust             1.161e-04  5.418e-04
## Condition70% Increasing:Confidence:Trust             -4.936e-05  5.638e-04
## Reliability:Confidence:Trust                          4.127e-06  4.980e-06
## Condition70% Increasing:Reliability:Confidence:Trust -3.638e-07  6.583e-06
##                                                      t value
## (Intercept)                                           -0.267
## Condition70% Increasing                               -0.413
## Reliability                                            0.232
## Confidence                                             0.393
## Trust                                                  0.914
## Condition70% Increasing:Reliability                    0.347
## Condition70% Increasing:Confidence                     0.529
## Reliability:Confidence                                -0.250
## Condition70% Increasing:Trust                         -0.054
## Reliability:Trust                                     -0.761
## Confidence:Trust                                      -0.926
## Condition70% Increasing:Reliability:Confidence        -0.505
## Condition70% Increasing:Reliability:Trust              0.214
## Condition70% Increasing:Confidence:Trust              -0.088
## Reliability:Confidence:Trust                           0.829
## Condition70% Increasing:Reliability:Confidence:Trust  -0.055

## 
## Correlation matrix not shown by default, as p = 16 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

tab_model(m70_2)

	Reliance
Predictors	Estimates	CI	p
(Intercept)	-0.68	-5.72 – 4.35	0.789
Condition [70% Increasing]	-1.41	-8.13 – 5.31	0.680
Reliability	0.01	-0.05 – 0.07	0.817
Confidence	0.01	-0.05 – 0.08	0.695
Trust	0.03	-0.04 – 0.10	0.361
Condition [70% Increasing] × Reliability	0.01	-0.07 – 0.09	0.729
Condition [70% Increasing] × Confidence	0.02	-0.06 – 0.11	0.597
Reliability × Confidence	-0.00	-0.00 – 0.00	0.802
Condition [70% Increasing] × Trust	-0.00	-0.09 – 0.09	0.957
Reliability × Trust	-0.00	-0.00 – 0.00	0.447
Confidence × Trust	-0.00	-0.00 – 0.00	0.355
(Condition [70% Increasing] × Reliability) × Confidence	-0.00	-0.00 – 0.00	0.614
(Condition [70% Increasing] × Reliability) × Trust	0.00	-0.00 – 0.00	0.830
(Condition [70% Increasing] × Confidence) × Trust	-0.00	-0.00 – 0.00	0.930
(Reliability × Confidence) × Trust	0.00	-0.00 – 0.00	0.408
(Condition [70% Increasing] × Reliability × Confidence) × Trust	-0.00	-0.00 – 0.00	0.956
Random Effects
σ²	0.03
τ₀₀ _Participant	0.10
ICC	0.79
N _Participant	81
Observations	486
Marginal R² / Conditional R²	0.035 / 0.798

Visualizations

Aparently othing in the model matters…. so no visuals

Performance

Model

# Everything Model
m70_3 <- lmer(data = data_long_70, Performance_After ~ Condition * Reliability * Confidence * Trust * Reliance * (1 | Participant))

## Warning: Some predictor variables are on very different scales: consider
## rescaling

summary(m70_3)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Performance_After ~ Condition * Reliability * Confidence * Trust *  
##     Reliance * (1 | Participant)
##    Data: data_long_70
## 
## REML criterion at convergence: -707.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.2430 -0.4611  0.0343  0.5755  2.7041 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Participant (Intercept) 0.006763 0.08224 
##  Residual                0.003617 0.06014 
## Number of obs: 486, groups:  Participant, 81
## 
## Fixed effects:
##                                                                 Estimate
## (Intercept)                                                   -1.872e+00
## Condition70% Increasing                                        5.126e+00
## Reliability                                                    2.960e-02
## Confidence                                                     4.062e-02
## Trust                                                          2.489e-02
## Reliance                                                       3.808e+00
## Condition70% Increasing:Reliability                           -5.661e-02
## Condition70% Increasing:Confidence                            -7.029e-02
## Reliability:Confidence                                        -4.254e-04
## Condition70% Increasing:Trust                                 -5.955e-02
## Reliability:Trust                                             -3.704e-04
## Confidence:Trust                                              -3.922e-04
## Condition70% Increasing:Reliance                              -6.733e+00
## Reliability:Reliance                                          -5.343e-02
## Confidence:Reliance                                           -6.733e-02
## Trust:Reliance                                                -4.612e-02
## Condition70% Increasing:Reliability:Confidence                 7.257e-04
## Condition70% Increasing:Reliability:Trust                      7.681e-04
## Condition70% Increasing:Confidence:Trust                       7.991e-04
## Reliability:Confidence:Trust                                   5.083e-06
## Condition70% Increasing:Reliability:Reliance                   8.649e-02
## Condition70% Increasing:Confidence:Reliance                    7.250e-02
## Reliability:Confidence:Reliance                                8.483e-04
## Condition70% Increasing:Trust:Reliance                         6.773e-02
## Reliability:Trust:Reliance                                     8.039e-04
## Confidence:Trust:Reliance                                      6.924e-04
## Condition70% Increasing:Reliability:Confidence:Trust          -9.443e-06
## Condition70% Increasing:Reliability:Confidence:Reliance       -8.890e-04
## Condition70% Increasing:Reliability:Trust:Reliance            -1.110e-03
## Condition70% Increasing:Confidence:Trust:Reliance             -6.727e-04
## Reliability:Confidence:Trust:Reliance                         -1.054e-05
## Condition70% Increasing:Reliability:Confidence:Trust:Reliance  1.096e-05
##                                                               Std. Error
## (Intercept)                                                    2.074e+00
## Condition70% Increasing                                        2.554e+00
## Reliability                                                    2.533e-02
## Confidence                                                     2.577e-02
## Trust                                                          2.631e-02
## Reliance                                                       4.606e+00
## Condition70% Increasing:Reliability                            3.013e-02
## Condition70% Increasing:Confidence                             3.111e-02
## Reliability:Confidence                                         3.180e-04
## Condition70% Increasing:Trust                                  3.499e-02
## Reliability:Trust                                              3.188e-04
## Confidence:Trust                                               3.091e-04
## Condition70% Increasing:Reliance                               6.785e+00
## Reliability:Reliance                                           5.550e-02
## Confidence:Reliance                                            5.501e-02
## Trust:Reliance                                                 5.792e-02
## Condition70% Increasing:Reliability:Confidence                 3.706e-04
## Condition70% Increasing:Reliability:Trust                      4.055e-04
## Condition70% Increasing:Confidence:Trust                       4.006e-04
## Reliability:Confidence:Trust                                   3.777e-06
## Condition70% Increasing:Reliability:Reliance                   7.773e-02
## Condition70% Increasing:Confidence:Reliance                    8.052e-02
## Reliability:Confidence:Reliance                                6.627e-04
## Condition70% Increasing:Trust:Reliance                         8.632e-02
## Reliability:Trust:Reliance                                     6.974e-04
## Confidence:Trust:Reliance                                      6.640e-04
## Condition70% Increasing:Reliability:Confidence:Trust           4.676e-06
## Condition70% Increasing:Reliability:Confidence:Reliance        9.234e-04
## Condition70% Increasing:Reliability:Trust:Reliance             9.870e-04
## Condition70% Increasing:Confidence:Trust:Reliance              9.970e-04
## Reliability:Confidence:Trust:Reliance                          7.993e-06
## Condition70% Increasing:Reliability:Confidence:Trust:Reliance  1.140e-05
##                                                               t value
## (Intercept)                                                    -0.902
## Condition70% Increasing                                         2.007
## Reliability                                                     1.169
## Confidence                                                      1.576
## Trust                                                           0.946
## Reliance                                                        0.827
## Condition70% Increasing:Reliability                            -1.879
## Condition70% Increasing:Confidence                             -2.259
## Reliability:Confidence                                         -1.338
## Condition70% Increasing:Trust                                  -1.702
## Reliability:Trust                                              -1.162
## Confidence:Trust                                               -1.269
## Condition70% Increasing:Reliance                               -0.992
## Reliability:Reliance                                           -0.963
## Confidence:Reliance                                            -1.224
## Trust:Reliance                                                 -0.796
## Condition70% Increasing:Reliability:Confidence                  1.958
## Condition70% Increasing:Reliability:Trust                       1.894
## Condition70% Increasing:Confidence:Trust                        1.995
## Reliability:Confidence:Trust                                    1.346
## Condition70% Increasing:Reliability:Reliance                    1.113
## Condition70% Increasing:Confidence:Reliance                     0.900
## Reliability:Confidence:Reliance                                 1.280
## Condition70% Increasing:Trust:Reliance                          0.785
## Reliability:Trust:Reliance                                      1.153
## Confidence:Trust:Reliance                                       1.043
## Condition70% Increasing:Reliability:Confidence:Trust           -2.019
## Condition70% Increasing:Reliability:Confidence:Reliance        -0.963
## Condition70% Increasing:Reliability:Trust:Reliance             -1.124
## Condition70% Increasing:Confidence:Trust:Reliance              -0.675
## Reliability:Confidence:Trust:Reliance                          -1.318
## Condition70% Increasing:Reliability:Confidence:Trust:Reliance   0.962

## 
## Correlation matrix not shown by default, as p = 32 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

tab_model(m70_3)

	Performance After
Predictors	Estimates	CI	p
(Intercept)	-1.87	-5.95 – 2.20	0.367
Condition [70% Increasing]	5.13	0.11 – 10.15	0.045
Reliability	0.03	-0.02 – 0.08	0.243
Confidence	0.04	-0.01 – 0.09	0.116
Trust	0.02	-0.03 – 0.08	0.345
Reliance	3.81	-5.24 – 12.86	0.409
Condition [70% Increasing] × Reliability	-0.06	-0.12 – 0.00	0.061
Condition [70% Increasing] × Confidence	-0.07	-0.13 – -0.01	0.024
Reliability × Confidence	-0.00	-0.00 – 0.00	0.182
Condition [70% Increasing] × Trust	-0.06	-0.13 – 0.01	0.089
Reliability × Trust	-0.00	-0.00 – 0.00	0.246
Confidence × Trust	-0.00	-0.00 – 0.00	0.205
Condition [70% Increasing] × Reliance	-6.73	-20.07 – 6.60	0.322
Reliability × Reliance	-0.05	-0.16 – 0.06	0.336
Confidence × Reliance	-0.07	-0.18 – 0.04	0.222
Trust × Reliance	-0.05	-0.16 – 0.07	0.426
(Condition [70% Increasing] × Reliability) × Confidence	0.00	-0.00 – 0.00	0.051
(Condition [70% Increasing] × Reliability) × Trust	0.00	-0.00 – 0.00	0.059
(Condition [70% Increasing] × Confidence) × Trust	0.00	0.00 – 0.00	0.047
(Reliability × Confidence) × Trust	0.00	-0.00 – 0.00	0.179
(Condition [70% Increasing] × Reliability) × Reliance	0.09	-0.07 – 0.24	0.266
(Condition [70% Increasing] × Confidence) × Reliance	0.07	-0.09 – 0.23	0.368
(Reliability × Confidence) × Reliance	0.00	-0.00 – 0.00	0.201
(Condition [70% Increasing] × Trust) × Reliance	0.07	-0.10 – 0.24	0.433
(Reliability × Trust) × Reliance	0.00	-0.00 – 0.00	0.250
(Confidence × Trust) × Reliance	0.00	-0.00 – 0.00	0.298
(Condition [70% Increasing] × Reliability × Confidence) × Trust	-0.00	-0.00 – -0.00	0.044
(Condition [70% Increasing] × Reliability × Confidence) × Reliance	-0.00	-0.00 – 0.00	0.336
(Condition [70% Increasing] × Reliability × Trust) × Reliance	-0.00	-0.00 – 0.00	0.262
(Condition [70% Increasing] × Confidence × Trust) × Reliance	-0.00	-0.00 – 0.00	0.500
(Reliability × Confidence × Trust) × Reliance	-0.00	-0.00 – 0.00	0.188
(Condition [70% Increasing] × Reliability × Confidence × Trust) × Reliance	0.00	-0.00 – 0.00	0.337
Random Effects
σ²	0.00
τ₀₀ _Participant	0.01
ICC	0.65
N _Participant	81
Observations	486
Marginal R² / Conditional R²	0.375 / 0.782

Visualizations

# performance by condition
# g1 <- ggplot(data_long_70, aes(x=Condition_num, y=Performance_After)) + 
#   geom_smooth(mehtod='lm') +
#   geom_beeswarm() +
#   theme_classic() +
#   theme(plot.title = element_text(size=title_size)) +
#   ylim(0, 1)
# print(g1)

flexplot(data = data_long_70, Performance_After ~ Condition, method = 'lm')

# Condition by Confidence
flexplot(data = data_long_70, Performance_After ~ Condition + Confidence, method = 'lm')

g2 <- ggplot(data_long_70, aes(x=Confidence, y=Performance_After, color=Condition)) + 
  geom_smooth(alpha = 0.5, method = 'lm') + 
  geom_point() +
  theme_classic() +
  labs(title = "Performance After by Confidence by Condition", x = "Confidence", y = "Performance After") +
  theme(plot.title = element_text(size=title_size)) +
  xlim(0, 100) + 
  ylim(0, 1)
print(g2)

## `geom_smooth()` using formula = 'y ~ x'

# Condition by Confidence by Trust
flexplot(data = data_long_70, Performance_After ~ Confidence + Trust | Condition, method = 'lm')

flexplot(data = data_long_70, Performance_After ~ Trust + Condition | Confidence, method = 'lm')

# Condition by Reliability, by Confidence, by Trust
flexplot(data = data_long_70, Performance_After ~ Trust + Confidence | Condition + Reliability_factor, method = 'lm')

LME_Analysis

Chris Holland

2024-04-18

Load Data

Basic Visuals

Histograms

Correlations

Data Checks

50% Models

Trust

Model

Visualizations

Dependence (Reliance)

Model

Visualizations

Performance

Model

Visualizations

70% Models

Trust

Model

Visualizations

Dependence (Reliance)

Model

Visualizations

Performance

Model

Visualizations